Simplify (8x^2y^2-9x^2y+9y)-(6x^2y-xy^2+4y)

$(8 x^{2} y^{2} - 9 x^{2} y + 9 y) - (6 x^{2} y - x y^{2} + 4 y)$

Simplify each term.

Apply the distributive property.

$8 x^{2} y^{2} - 9 x^{2} y + 9 y - (6 x^{2} y) - (- x y^{2}) - (4 y)$

Simplify.

Multiply $6$ by $- 1$ .

$8 x^{2} y^{2} - 9 x^{2} y + 9 y - 6 (x^{2} y) - (- x y^{2}) - (4 y)$

Multiply $- (- x y^{2})$ .

Multiply $- 1$ by $- 1$ .

$8 x^{2} y^{2} - 9 x^{2} y + 9 y - 6 (x^{2} y) + 1 (x y^{2}) - (4 y)$

Multiply $x$ by $1$ .

$8 x^{2} y^{2} - 9 x^{2} y + 9 y - 6 (x^{2} y) + x y^{2} - (4 y)$

Multiply $4$ by $- 1$ .

$8 x^{2} y^{2} - 9 x^{2} y + 9 y - 6 (x^{2} y) + x y^{2} - 4 y$

$8 x^{2} y^{2} - 9 x^{2} y + 9 y - 6 x^{2} y + x y^{2} - 4 y$

Simplify by adding terms.

Subtract $6 x^{2} y$ from $- 9 x^{2} y$ .

$8 x^{2} y^{2} - 15 x^{2} y + 9 y + x y^{2} - 4 y$

Subtract $4 y$ from $9 y$ .

$8 x^{2} y^{2} - 15 x^{2} y + x y^{2} + 5 y$